Geodesic
$\pi a_1$ Transitions and low-energy limit in the linear sigma model
Teoretičeskaâ i matematičeskaâ fizika, Tome 86 (1991) no. 3, pp. 385-390 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of obtaining the correct low-energy limit in the linear sigma model with participation of vector and axial-vector mesons is discussed. In a naive treatment of the tree approximation, for example, in $\pi\pi$ scattering, the diagrams with intermediate scalar and vector mesons may lead to double counting in the scattering lengths. For the case of the scattering amplitudes and the semileptonic decay $\tau\to\nu_\tau 3\pi$ it is shown that this problem can be solved by taking into account $\pi a_1$ transitions at the external ends of the corresponding meson vertices. 
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     title = {$\pi a_1${~Transitions} and low-energy limit in the linear sigma model},
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M. K. Volkov; A. A. Osipov. $\pi a_1$ Transitions and low-energy limit in the linear sigma model. Teoretičeskaâ i matematičeskaâ fizika, Tome 86 (1991) no. 3, pp. 385-390. http://geodesic.mathdoc.fr/item/TMF_1991_86_3_a7/

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